Electronic properties ofδ-doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method

Abstract

The Thomas-Fermi-Dirac (TFD) approximation and an sp 3 d 5 s * tight binding method were used to calculate the electronic properties of a δ-doped phosphorus layer in silicon. This self-consistent model improves on the computational efficiency of "more rigorous" empirical tight binding and ab initio density functional theory models without sacrificing the accuracy of these methods. The computational efficiency of the TFD model provides improved scalability for large multi-atom simulations, such as of nanoelectronic devices that have experimental interest. We also present the first theoretically calculated electronic properties of a δ-doped phosphorus layer in germanium as an application of this TFD model.

Ab initio electronic properties of dual phosphorus monolayers in silicon

“…The time is thus ripe to attend to possible three-dimensional architectures built from phosphorus in silicon. Although Si:P single-donor physics is well understood, and several studies have been completed on single-structure epitaxial Si: δ P circuit components (such as infinite single monolayers [ 10 - 17 ], single thicker layers [ 18 , 19 ], epitaxial dots [ 20 ], and nanowires [ 1 , 21 ]), a true extension studying interactions between device building blocks in the third dimension is currently missing.…”

Revealing quantum effects in highly conductive δ-layer systems

“…Electronic structure and conductive properties of Si:P δ-layer systems, which consists of a thin, highly phosphorous (P) doped 2D sheet layer embedded in lightly doped silicon, as shown in Fig. 1a, have been a subject of active studies for the last several decades [7][8][9][10][11][12][13][14][15][16][17][18] leading to applications in quantum computing 19,20 and advanced microelectronic devices 6,21,22 . Recent angle-resolved photoemission spectroscopy (ARPES) measurements [23][24][25][26][27] revealed the existence of shallow conductive states that determines the conductive properties of these systems.…”

“…Naturally, particular attention has also been given to numerical studies of the electronic structure of δ-layer systems. Previous computational studies of these systems based on either effective mass 16 , tight-binding 15,18,28 or density functional theory 13,14,17 formalisms can be classified into two categories: truly closedsystem approaches, with the Dirichlet-type boundary conditions for the wave-function, and approaches with periodic boundary conditions along the propagation direction. However, in both cases, if the conductive properties of the system need to be extracted, this principally cannot be done directly from the quantum-mechanical flux.…”

Determining the Electronic Confinement of a Subsurface Metallic State

“…13 Such physical confinement gives rise to a nearly-free electron-like occupied band dispersion, the calculation of which has been the centre of much effort. [13][14][15][16][17][18][19] The occupied bandstructure has also recently been verified by photoemission spectroscopy (PES). 6,20 The experimental verification is only possible because of a strongly enhanced photoemission intensity which occurs when an electron from a two dimensional (2D) initial state is photo-emitted via a well matched bulk-like final state.…”

“…The physical placement of the dopant atoms can be controlled and measured, 10,11,22 but the electronic confinement, which is the key to understanding electronic parameters such as valley splitting, has been accessible only through calculations. 6,[13][14][15][16][17][18][19] Here we show that the strongly peaked photoemission enhancement which allows the δ-layer states to be visible, also allows the physical profile of their wavefunction to be extracted.…”